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Steiner construction

Steiner construction
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2018-04-06 11:07
AngleTransformationGeometric ConstructionLocus
In collections Conic sections
This example demonstrates the geometric construction of Steiner points to connect three points with the shortest path. It involves core math concepts like geometric construction, angles, rotation, and similarity transformations. The construction uses GeoGebra commands such as Line, Intersect, and Locus, with objects like points A, B, f, C, D, t, E, F, h, i, G, loc1, H, g, I. Suitable for high school and above students learning geometric constructions and optimization problems.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Line(D, F) → h
  3. Line(C, E) → i
  4. Intersect(h, i) → G
  5. Locus(G, t) → loc1
  6. Line(A, H) → g
  7. Intersect(g, h) → I

AI Drawing Prompt Reference

Construct the Steiner points for three points A, B, and C by first drawing lines AB, DE, and CF, then finding their intersection point G, drawing line AG and finding its intersection with line DE to get point I, and finally drawing the locus of point G as loc1.
The prompt above was compiled from the original drawing commands and is for reference only.